-x^2-20.5x-61.5=0

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Solution for -x^2-20.5x-61.5=0 equation:


Simplifying
-1x2 + -20.5x + -61.5 = 0

Reorder the terms:
-61.5 + -20.5x + -1x2 = 0

Solving
-61.5 + -20.5x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
61.5 + 20.5x + x2 = 0

Move the constant term to the right:

Add '-61.5' to each side of the equation.
61.5 + 20.5x + -61.5 + x2 = 0 + -61.5

Reorder the terms:
61.5 + -61.5 + 20.5x + x2 = 0 + -61.5

Combine like terms: 61.5 + -61.5 = 0.0
0.0 + 20.5x + x2 = 0 + -61.5
20.5x + x2 = 0 + -61.5

Combine like terms: 0 + -61.5 = -61.5
20.5x + x2 = -61.5

The x term is 20.5x.  Take half its coefficient (10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
20.5x + 105.0625 + x2 = -61.5 + 105.0625

Reorder the terms:
105.0625 + 20.5x + x2 = -61.5 + 105.0625

Combine like terms: -61.5 + 105.0625 = 43.5625
105.0625 + 20.5x + x2 = 43.5625

Factor a perfect square on the left side:
(x + 10.25)(x + 10.25) = 43.5625

Calculate the square root of the right side: 6.600189391

Break this problem into two subproblems by setting 
(x + 10.25) equal to 6.600189391 and -6.600189391.


Subproblem 1
x + 10.25 = 6.600189391

Simplifying
x + 10.25 = 6.600189391

Reorder the terms:
10.25 + x = 6.600189391

Solving
10.25 + x = 6.600189391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = 6.600189391 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = 6.600189391 + -10.25
x = 6.600189391 + -10.25

Combine like terms: 6.600189391 + -10.25 = -3.649810609
x = -3.649810609

Simplifying
x = -3.649810609


Subproblem 2
x + 10.25 = -6.600189391

Simplifying
x + 10.25 = -6.600189391

Reorder the terms:
10.25 + x = -6.600189391

Solving
10.25 + x = -6.600189391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = -6.600189391 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = -6.600189391 + -10.25
x = -6.600189391 + -10.25

Combine like terms: -6.600189391 + -10.25 = -16.850189391
x = -16.850189391

Simplifying
x = -16.850189391


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.649810609, -16.850189391}

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